The present invention relates generally to the field of machine tools. More specifically, the present invention relates generally to methods of and apparatuses for suppressing or preventing chatter in a machine tool assembly by modulating the mechanical impedance (time-varying impedance) of a component of the machine tool assembly.
The literature discussing regenerative chatter associated with metal cutting is extensive. Chatter is a regenerative instability associated with the playback of irregularities on the workpiece (machined part) from previous cuts to the machine (cutting) tool. FIG. 1A is a representative depiction of the chatter associated with machine tool assembly 400 and operation thereof, which, as illustrated, can be an undesirable nuisance to one's ears. Encountered in many types of metal removal processes, chatter is a dangerous condition that results from the interaction of the cutting dynamics with the modal characteristics of the machine-workpiece assembly. Machine tool vibrations are recorded on the surface of the workpiece during metal removal, imposing a waviness that alters the chip thickness during subsequent cutting passes. Deviations from the nominal chip thickness effect changes in the cutting force which, under certain conditions, can further excite vibrations. The costs of chatter include the variability of end product, waste of parts, tool breakage or wear, and reduced production.
The mechanical process appears to be well understood. (See, e.g., H. E. Merritt, "Theory of Self-Excited Machine Tool Chatter," Journal of Engineering for Industry, Vol. 87, pp. 447-453, November 1965; R. A. Thompson, "On the Doubly Regenerative Stability of a Grinder: The Theory of Chatter Growth," Journal of Engineering for Industry, Vol. 108, pp.75-82, May 1986; and J. Tlusty and F. Ismail, "Special Aspects of chatter in Milling," Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 105, pp. 24-32, May 1 986.) The physics of the problem can be understood qualitatively through analogy with the old Edison wax phonographs as depicted in FIG. 1; the playing and recording of a wax phonograph record 15 is analogous to the machine tool chatter process. Referring to FIG. 1, as the track moves under the needle 10, undulations within the groove 5 (dotted line) excite vibration in a speaker and sound is conveyed into the air. Similarly, sounds in the air are conveyed through the speaker and needle 10 into the wax of the record 15. Any mechanical oscillations (resonances) in the mechanical system will also be recorded on the record 15. If mechanical resonances are inadvertently recorded, then playback of the record 15 could further excite those resonances and the large signal will be re-recorded into the wax. This regenerative process is referred to as chatter. An illustration of this effect in milling is shown in FIG. 2. The kinematics of the cutting process 200 illustrates the manner in which surface texture due to tool oscillations on previous cuts contributes to the forces on the cutting tool 410. Oscillation or vibration of cutting tool 410 imposes a waviness (represented by lines 230 and 235) on the surface of workpiece 210 during each pass of the cutting tooth 220. (The ideal cut is represented by dotted lines 260 and 265.) The waviness (lines 230 and 235) imposed then excites tool vibration during the subsequent tool pass by altering the nominal chip thickness and the resultant cutting forces. Surface waviness can further excite vibrations by altering the instantaneous chip thickness, h (where h=h.sub.nominal +z(t)-z(t-T) (see FIG. 2). The stability of cutting conditions depends on the interaction of the current and past vibrations.
Additionally, chatter avoidance and suppression have been extensively considered. (See, e.g., S. K. Choudhury and M. S. Sharath, "On Line Control of Machine Tool Vibration During Turning Operation," Journal of Material Processing Technology, Vol. 47, pp. 251-259, 1995; S. Smith and T. Delio, "Sensor Based Chatter Detection and Avoidance by Spindle Speed Selection," Journal of Dynamic Systems, Measurement, and Control, Vol. 114, pp. 486-492, 1992; and S. G. Tewani, B. L. Walcott, and K. E. Rouch, "Cutting Process Stability of A Boring Bar with Active Dynamic Absorber," Proceedings of the 13th Biennial Conference on Mechanical Vibration and Noise, DE Vol. 37, pp. 205-213, 1991.) The primary approaches are suggested by the classical stability chart for turning processes, which is defined by the dynamic stiffness of the cutting tool. A nominal stability chart 300 is shown in FIG. 3, which displays a cutting stability boundary (represented by curve 310) as a function of the cutting-tool spindle speed (rpm) and axial depth-of-cut (mm). In FIG. 3, all cutting processes that fall below curve 310 represent stable cutting conditions. Conversely, all cutting processes that fall above the curve 310 represent unstable cutting conditions (regenerative chatter). Several techniques have been explored in the past for maintaining cutting stability including:
(1) Small depth-of-cut. Taking such shallow cuts that the process stays within the stability domain (see FIG. 3) regardless of cutting speed; PA1 (2) Speed selection. Adjusting the depth-of-cut for a particular cutting speed to stay below envelope 340 of stability curve 310; PA1 (3) Low tool speed. Adjusting the speed to remain within stability lobes for a given depth of cut (the CRACK method is a version of this technique (See S. Smith and T. Delio, "Sensor Based Chatter Detection and Avoidance by Spindle Speed Selection," Journal of Dynamic Systems, Measurement, and Control, Vol. 114, pp. 486-492, 1992.)); and PA1 (4) High Stiffness/Damping. Maximizing the dynamic stiffness of the cutting machine and the part support through design, which results in raising the stability curve in the "depth-of-cut" direction and increasing the number of stable process conditions.
Another method, not suggested by nominal stability chart 300 of FIG. 3, is that of perturbing the cutting speed about the nominal speed to disrupt the modulation of current and previous tool vibrations that can lead to chatter. (See K. Jemelniak and A. Widota, "Suppression of Self-Excited Vibration by Spindle Speed Variation Method," International Journal of Machine Tool Design and Research," Vol. 24, No.3, pp. 207-214, 1984.) This process can be summarized by a horizontal line segment 320 on nominal stability chart 300, with the cutting speed moving cyclically from side to side.